ON THE LEAST PRIME IN AN ARITHMETICAL PROGRESSION AND THEOREMS CONCERNING THE ZEROS OF DIRICHLET'S L-FUNCTIONS

Let D be a sufficiently large integer, and P（D, K） the least prime in the progression {Dn+K:n∈N, 0<K≤D, （D,K）=1}. In 1934, S. Chowla in J. Indian Math. Soc., 1（1934）, 1—3 conjectured that P（D, K）≤D1+ε for any positive number ε. In 1937, P. Turan proved that under